Melisa Hendrata, P.K. Subramanian
Department of Mathematics
California State University
Los Angeles, 5151, State University Drive, Los Angeles, CA 90032, USA

Abstract. In the minimization of real valued functions, Newton's algorithm is often combined with a line search method. Grippo et al [SIAM J. Numer. Anal., Vol. 23, No. 4] first suggested a nonmonotone stepsize selection rule based on the maximum of a fixed set of previous function values. In this paper we introduce the notion of relaxing functions and suggest several other nonmonotone procedures using a modified Newton direction. Computational performance on several standard test problems is presented, which shows that the proposed models are viable alternatives.

Received: November 24, 2012

AMS Subject Classification: 90, 90-08

Key Words and Phrases: Newton's method, Armijo line search, nonmonotone line search, global optimization

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